Elamur Groupantsoptimization-methods
The groupant beside models/optimization-methods.groupant in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial source model | forward |
| ast | not materialized | |
| composition | partial source model | composition |
| cost | partial source model | cost |
| descriptant | partial source model | epoch-memory |
| invariant | partial source model | invariant |
| tests | bounded executed | checks |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
optimization-methods-behavior-complement | behavior_complement | partial source model | behavior-complement |
optimization-methods-reverse-reconstruction | reverse_reconstruction | partial source model | reverse-reconstruction |
optimization-methods-line-restriction | directional_derivative_transport | partial source model | line-restriction |
optimization-methods-normal-cone | constrained_stationarity_relation | partial source model | normal-cone |
optimization-methods-lasso-threshold | orthogonal_proximal_relation | partial source model | lasso-threshold |
Model text
model
optimization-methods
forward
Bounded scalar minimization and sufficient-decrease search, box/simplex quadratic optimization, and coordinate Lasso descent.
invariant
Quadratic objective is .5xQx-linearx; Lasso is .5||Ax-y||²+lambda||x||1. Scalar bracket, feasible set, stationarity measure and termination status remain tagged.
cost
Scalar O(k) callbacks; dense quadratic O(kn²), Lasso O(km*n) plus objective/residual checks; leaf dimensions and iteration caps apply.
composition
Directional quadratic restrictions connect Armijo to Brent; QR normal equations connect least squares to constrained optimization on fixtures with feasible minimizer; orthogonal Lasso reduces to soft threshold.
epoch-memory
Wave20, 2026-10-30. Models retain real-arithmetic assumptions separately from native finite checks. Kernels are library tools, not automatically adopted into training or inference.
checks
["qr_and_constrained_optimizers_join_known_quadratic","brent_and_armijo_join_scalar_quadratic","lasso_and_triangular_identity_join_soft_threshold_solution"]
limitations
Scalar unimodality/differentiability are caller premises. Projected step residual and FW floating gap are not unconditional distance/certified objective bounds. Tightened PSD admission rejects some valid PSD matrices.
catalog
Typed family relations
Each relation keeps its own domain and assurance.
behavior-complement
Type: behavior_complement.
For real convex quadratic minimization on C, exclude infeasible x or b-Qx outside N_C(x); for Lasso exclude Aᵀ(Ax-y)+lambda*s!=0 for every s in the L1 subgradient. For a supplied scalar restriction, exclude an Armijo step violating its sufficient-decrease inequality and a claimed global Brent minimizer outside the stipulated unimodal target. Native finite reports instead obey rounded transition/stopping relations: box projected-step residual, simplex FW gap and Lasso KKT residual are distinct. Exclude switching the minus-linear convention, using objective error as coordinate error, exceeding callback budget or relabeling exhausted/stagnated reports. Native Converged does not assert the exact real KKT equalities.
reverse-reconstruction
Type: reverse_reconstruction.
For fixed real Q,C and feasible optimizer x, compatible linear terms lie in Qx+N_C(x); thus a boundary optimizer generally does not identify b. Identity-design Lasso with lambda fixed gives y_i=x_i+lambdasign(x_i) for nonzero x_i, while x_i=0 admits every y_i in [-lambda,lambda]. General designs admit y with Aᵀ(y-Ax) in lambdapartial||x||1, including null(Aᵀ) perturbations. Brent and Armijo observations retain many callbacks agreeing at the sampled points but differing elsewhere; a step does not recover its direction or original objective. These are real target fibers; matching a native report additionally requires matching its rounded path, validation and status.
line-restriction
Type: directional_derivative_transport.
For q(x)=.5xQx-bx and p, derivative at t0 is pᵀ(Qx-b); Armijo requires negative supplied slope and evaluates q(x+t*p). Brent shares the same restricted objective under a valid unimodal bracket.
normal-cone
Type: constrained_stationarity_relation.
Real box optimum obeys 0 in Qx-b+N_box(x); simplex FW gap=max_vertex gradient·(x-vertex) vanishes at optimum for convex q. Different residuals cannot be equated as numerical error.
lasso-threshold
Type: orthogonal_proximal_relation.
Identity design yields x_i=sign(y_i)max(|y_i|-lambda,0). Nonzero outputs reconstruct y by adding lambda sign; zero output retains interval[-lambda,lambda]. General design couples coordinates.
wave20-evidence
Family evidence — 2026-10-30
This family binds ten implementation/test sources. Named joins ["qr_and_constrained_optimizers_join_known_quadratic","brent_and_armijo_join_scalar_quadratic","lasso_and_triangular_identity_join_soft_threshold_solution"] in algorithms/tests/composition_wave20.rs pass four times within the 695-check algorithm suite.
Forward: Bounded scalar minimization and sufficient-decrease search, box/simplex quadratic optimization, and coordinate Lasso descent.
Invariant: Quadratic objective is .5xQx-linearx; Lasso is .5||Ax-y||²+lambda||x||1. Scalar bracket, feasible set, stationarity measure and termination status remain tagged.
Cost: Scalar O(k) callbacks; dense quadratic O(kn²), Lasso O(km*n) plus objective/residual checks; leaf dimensions and iteration caps apply.
Assumptions: Scalar unimodality/differentiability are caller premises. Projected step residual and FW floating gap are not unconditional distance/certified objective bounds. Tightened PSD admission rejects some valid PSD matrices.
Integrated evidence records actual receipts. Leaf oracles remain separate from cross-implementation agreement; family membership cannot verify unchecked callback premises or a shared error budget.
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